I have been asked this on more than one occasion, so the approx costings (excluding fluctuating exchange rate and additional equipment purchased) to fly from the UK to Montana and complete a big game hunt, self guided:
Air fare £900 including extra bag for rifle (Delta, as BA wanted to rip me off with an 'inspection of rifle')
Car hire for 2 weeks £332 Alamo intermediate SUV (Rav 4 or equivalent)
First and last night in hotel £98 (remainder of the time i will be sleeping in the car or camping out, unless it drops to -23c like it did last time!)
Big game tag £600
Of course on top of this is spending money, fuel and food which are personal things, so excluding that the approx total cost is:
Any questions please feel free to ask, all except where i will be hunting, you can do your own research on that one!